#### Summary

Closed economies are defined as countries that are self-sufficient and autarkic. A widely used analogy by Economics professors is Robinson Crusoe’s island, since Crusoe was unable to trade. This one-man economy is the easiest way to understand closed economies.The IS-LM (*Investment* Savings-Liquidity preference Money supply) model focuses on the *equilibrium of the market* for *goods* and services, and the money market. It basically shows the relationship between *real output* and interest rates.

It was developed by *John R. Hicks*, based on *J. M. Keynes*’ “General Theory”, in which he analysed four markets: goods, labour, credit and money. This model, firstly named IS-LL, appeared in his article “Mr. Keynes and the Classics: a Suggested Interpretation”, published in 1937 in the journal Econometrica.

In order to understand how this model works, we’ll first see how the IS curve, which represents the equilibrium in the goods market, is defined. Then, the LM curve, which represents the equilibrium in the money market. Finally, we’ll analyse how the equilibrium is reached.

**IS curve: the market for goods and services**

In a closed economy, the equilibrium condition in the market for goods is that production (Y), is equal to the demand for goods, which is the sum of *consumption*, investment and *public spending*. This relationship is called IS. If we define consumption (*C*) as *C = C(Y-T)* where *T* corresponds to *taxes*, the equilibrium would be given by:

*Y = C (Y- T) + I + G*

We consider that investment is not constant, and we see that it depends mainly on two factors: the level of sales and interest rates. If the sales of a firm increase, it will need to invest in new production plants to raise *production*; it is a positive relation. With regard to interest rates, the higher they are, the more expensive investments are, so that the relationship between interest rates and investment is negative. The new relationship is expressed as follows (where *i* is the interest rate):

*Y = C (Y- T) + I (Y, i) + G*

If we keep in mind the equivalence between production and demand, which determines the equilibrium in the market for goods, and observe the effect of interest rates, we obtain the IS curve. This curve represents the value of equilibrium for any interest rate.

An increasing interest rate will cause a reduction in production through its effect on investment. Therefore, the curve has a negative slope. The adjacent graph shows this relationship.

**LM curve: the market for money**

The LM curve represents the relationship between liquidity and money. In a closed economy, the interest rate is determined by the equilibrium of supply and demand for money: *M/P=L(i,Y) *considering *M* the amount of money offered, *Y* real income and i real interest rate, being *L* the demand for money, which is function of *i* and *Y*.

The equilibrium of the money market implies that, given the amount of money, the interest rate is an increasing function of the output level. When output increases, the demand for money raises, but, as we have said, the money supply is given. Therefore, the interest rate should rise until the opposite effects acting on the demand for money are cancelled, people will demand more money because of higher income and less due to rising interest rates.

The slope of the curve is positive, contrary to what happened in the IS curve. This is because the slope reflects the positive relationship between output and interest rates.

**IS-LM model**

At any point of these curves the equilibrium condition in the corresponding market is true, but only at the point where the two curves intersect, both equilibrium conditions are satisfied. We can see this intersection in the following graph:

The IS and LM curves undertake changes due to many factors, such as different kinds of *economic policies*. These variations will explain the changes in the values of production and of interest rates taking place in the economies.

For instance, if there is an increase in government spending, which is considered a *fiscal policy*, the IS curve will shift to the right, as seen in the graph in the left. This happens because more government spending means more production for any interest rate. This shift, as seen in the adjacent graph, will consequently change the equilibrium from point E_{1} to point E_{2}, with a greater level of output, but also at greater interest rates.

On the other hand, if we consider a *monetary policy*, such as an increase in the money supply, the curve that shifts will be the LM curve, as seen in the graph in the right. An increase in the money supply will decrease the interest rate, shifting the LM curve to the right, thus increasing output.

**Monetarists’ views on the IS-LM model: **

*Monetarists* greatly criticized the IS-LM model, highlighting some different views regarding the *elasticity* (and therefore the slope) of both curves. In their opinion, the LM curve is very inelastic, while the IS curve is very elastic. The most important thing we derive from these different views is the different consequences and effectiveness of expansionary fiscal and monetary policies.

Monetarists argue that monetary policies are more effective. Take the same example as before, an increase in the money supply. This will shift the LM curve to the right, displacing the equilibrium from E_{1} to E_{2} in the figure below. However, monetarists consider also two other effects: direct and indirect wealth effect. The first one, also known as Pigouvian effect, considers that, because of the increase in money supply, people will consume more, shifting the IS curve and changing the equilibrium to point E_{3}. The second one considers that, because of the initial drop in the equilibrium interest rates, people will invest more, thus shifting even more the IS curve and changing the equilibrium to point E_{4}.

Now, monetarists are more sceptic than *Keynesians* about fiscal policy. This is because, as seen in the figure below, the initial shift of the IS curve (from point E_{1} to point E_{2}) will be partly offset by a second shift of the same curve. This, known as crowding-out, happens because the increase in government spending increases interest rates, which decreases the attractiveness of investment. Therefore, the more the government spends, the less private capital will be invested, which moves the equilibrium from point E_{2} to E_{3}. Also, because of higher output, money demand increases, which shifts the LM curve to the left, to point E_{4}.

Both views have a great army of researchers and professors defending them, as part of the modern division on such matters into two main doctrines: *New Keynesian Economics* and *New Classical Macroeconomics*. All the effects presented here must be taken into consideration when analysing the IS-LM model. However, it must be noted that some of these conclusions change when considering an open economy, which is analysed by the *IS-LM-BoP or Mundell-Fleming model*.